磁阻測量、居理溫度測量實驗

磁阻效應 磁阻  (H) 是被定義為樣品在磁場中電阻之改變量， 即  (H) =  (H) -  (H = 0) ，此處  (H) 是在磁場 H 下 樣品之電阻率。 材料有不同之磁阻, 其原因可來自 ; 電荷受羅倫茲力之作用而改變甚行進路徑造成電荷 與晶格間散射機率增加, 此時  (H) > 0 ; 受磁矩在磁場下電子自旋與磁矩間間散射狀態改變 的影響, 若樣品是鐵磁性材料, 其磁矩對電荷自旋之 散射機率會因為外加磁場之增加而減小, 此時  (H) < 0 。 其他物理原因。

X Z Y A B H J X Z H Y J (a) (b) A B 樣品置於外加磁場 H 之中, 若將電流 J 通於樣品, 此樣 品在磁場下產生磁阻效應。 (a) 為縱向磁阻效應 (H 之 方向平行於 J 之方向 );(b) 為橫向磁阻效應 (H 之方向垂直 於 J 之方向 )

Nd,Sr Mn O b (5.46 Å) c (7.7 Å) a (5.47 Å) 氧化物 Nd 1-X Sr X MnO 3 巨磁阻材料中 Nd, Sr, Mn 和 O 原子之排列情形， 此化合物之居禮溫度約在 230 K 。

NSMO and LCMO films show the Curie temperature at 222 K and 250 K respectively.

● The pattern for resistivity and Hall measurements ● The pattern for resistivity and Hall measurements V = V 3 -V 2 →Resistance V h = V 2 -V 1 →Hall coefficient

Temperature dependence of the longitudinal resistivity  xx for YBa 2 Cu 3 O y (YBCO) (1500 Å and NSMO (2100 Å) films. (b)

Nd 1-X Sr X MnO 3 薄膜在 (a) 不同磁場下電阻與溫度的相依行為 ; (b) 磁阻比與溫度 的相依行為

巨磁阻 Pr0.7Sr0.3MnO3 薄膜在溫度為 30 K 的電阻對角度  B 相依行為，  B 為磁場與 基座法線之夾角。由上而下的圖形外加磁場值分別為 600 G ， 2500 G ， 4500 G ， 5500 G ， 12.5 kG ， 20 kG 及 60 kG 。

Diamagnetism Paramagnetism Ferromagnetism Antiferromagnetism Others 磁性

Diamagnetism Diamagnetism is a form of magnetism which is only exhibited by a substance in the presence of an externally applied magnetic field. It is the result of changes in the orbital motion of electrons due to the application of an externally applied magnetic field. Applying a magnetic field creates a magnetic force on a moving electron in the form of F=qv x B. This force changes the centripetal force on the electron, causing it to either speed up or slow down in its orbital motion. This changed electron speed modifies the magnetic moment of the orbital in a direction against the external field.

Magnetic moment of Free Electrons or electrons in atoms) 1. The spin with which electrons are associated; Paramagnetic contribution to the magnetization Diamagnetic contribution to the magnetization Their orbital angular momentum about the nucleus; 3. The change in the orbital moment induced by an applied magnetic field. Note: Atoms with filled electron shells have zero spin and zero orbital moment.  The moments of atoms are associated with electrons in unfilled shells. 1. e-e- e-e- Nucleon H 3. I Nucleon

 PARAMAGNETISM Paramagnetism is the tendency of the atomic magnetic dipoles to align with an external magnetic field. This effect occurs due to quantum- mechanical spin as well as electron orbital angular momentum.

Paramagnetic materials exhibit magnetisation according to Curie's Law:Curie's Law where M is the resulting magnetisation; B is the magnetic flux density of the applied field, measured in tesla; T is absolute temperature, measured in kelvins and C is a material-specific Curie constant.

, if  B<<k B T Curie-Langevin law  PARAMAGNETISM Due to unfilled electrons, atoms will have a magnetic moment  We may also rewrite the Curie’s law for paramagnetism as  p = C/T

Metal Due to the Fermi gas of conduction electrons M = B  = = Independent of T Pauli parasmagnetism T F = Fermi temperature

Ferromagnetism

Ferromagnetism is a phenomenon by which a material can exhibit a spontaneous magnetization, and is one of the strongest forms of magnetism.magnetism Historically, the term "ferromagnet" was used for any material that could exhibit spontaneous magnetization: a net magnetic moment in the absence of an external magnetic field. This general definition is still in common use. magnetic field

Antiferromagnetism In materials that exhibit antiferromagnetism, the spins of magnetic electrons align in a regular pattern with neighboring spins pointing in opposite directions. This is the opposite of ferromagnetism.magneticelectronsspins ferromagnetism Generally, antiferromagnetic materials exhibit antiferromagnetism at a low temperature, and become disordered above a certain temperature; the transition temperature is called the Neel temperature. Above the Neel temperature, the material is typically paramagnetic.Neel temperatureparamagnetic

Antiferromagnets can also couple to ferromagnetic materials through a mechanism known as exchange anisotropy, in which the ferromagnetic film is either grown upon the antiferromagnet or annealed in an aligning magnetic field, causing the surface atoms of the ferromagnet to align with the surface atoms of the antiferromagnet. ferromagneticexchange anisotropy ferromagnetic ferromagnet This provides the ability to "pin" the orientation of a ferromagnetic film, which provides one of the main uses in so-called spin valves, which are the basis of magnetic sensors including modern hard drive read heads.ferromagneticspin valveshard drive

Ordered arrangements of spins A spontaneous magnetic moment exists even in zero applied magnetic field. Electron spins and magnetic moments are arranged in a regular manner.

 FERROMAGNETIC ORDER Above the Curie temperature T c, the spontaneous M vanishes. Curie-Weiss law  C = T c, T > T c

 FERROMAGNETIC ORDER

Vibrating Sample Magnetometer (VSM) SQUID Magnetometer Energy product  0 superparamagnetic small soft magnetic material large hard magnetic material Saturated Magnetization Magnetic Hysteresis Curve  FERROMAGNETIC ORDER

Temperature Dependence of the Saturation Magnetization If we omit the applied magnetic field and replace B by the molecular field B E = M, then For spin ½, M = N  tanh(μB/k B T) M = N  tanh(μ M /k B T)

 FERROMAGNETIC ORDER

 ANTIFERROMAGNETIC ORDER  = M/B a M = Magnetic moment per unit volume, B a = applied magnetic field.

 FERROMAGNETIC DOMAINS Energy is relatively high

 FERROMAGNETIC DOMAINS Domain Wall 10  200 nm

 FERROMAGNETIC DOMAINS The directions of magnetization of different domains need not be parallel. An arrangement of domains is tend to approximately zero resultant magnetic moment. Domains form also in antiferromagnetics, ferroelectrics, anti- ferroelectrics, and superconductors etc.

 SINGLE DOMAIN PARTICLES

MFM Magnetic Force Microscope AFM Atomic Force Microscope SiN tip STM Scanning Tunneling Microscope W/Pt tip SPM Surface Probe Microscope

 SINGLE DOMAIN PARTICLES